# AN AUGMENTED IIM FOR HELMHOLTZ/POISSON EQUATIONS ON IRREGULAR DOMAINS IN COMPLEX SPACE

@inproceedings{Zhang2015ANAI, title={AN AUGMENTED IIM FOR HELMHOLTZ/POISSON EQUATIONS ON IRREGULAR DOMAINS IN COMPLEX SPACE}, author={Sidong Zhang and Liu Zhilin}, year={2015} }

In this paper, an augmented immersed interface method has been developed for Helmholtz/Poisson equations on irregular domains in complex space. One of motivations of this paper is for simulations of wave scattering in different geometries. This paper is the first immersed interface method in complex space. The new method utilizes a combination of methodologies including the immersed interface method, a fast Fourier transform, augmented strategies, least squares interpolations, and the…

## 5 Citations

### Solving Interface Problems of the Helmholtz Equation by Immersed Finite Element Methods

- Computer ScienceCommunications on Applied Mathematics and Computation
- 2019

This article reports the explorations for solving interface problems of the Helmholtz equation by immersed finite elements (IFE) on interface independent meshes with partially penalized and discontinuous Galerkin IFE methods.

### Error Analysis of Symmetric Linear/Bilinear Partially Penalized Immersed Finite Element Methods for Helmholtz Interface Problems

- Mathematics, Computer ScienceJ. Comput. Appl. Math.
- 2021

### A fast high-order algorithm for the multiple cavity scattering

- MathematicsInt. J. Comput. Math.
- 2019

A fast high-order algorithm is proposed for solving the electromagnetic scattering from multiple cavities embedded in an infinite ground plane by means of a transparent boundary condition that results in a big system involving the Helmholtz equations with the coupled transparent boundary conditions, which is further reduced to a small system that includes only the coupling of the aperture system of each cavity.

### A locally second order symmetric method for discontinuous solution of Poisson's equation on uniform cartesian grids

- Computer ScienceComputers & Fluids
- 2020

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